This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained com-pression. The influence of the overlap length and patch thickness was evaluated. This loading gains a par-ticular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no trans-verse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling.